"Dimer model"의 두 판 사이의 차이
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| 118번째 줄: | 118번째 줄: | ||
* [http://arxiv.org/abs/math/0310195 Dimers, Tilings and Trees] | * [http://arxiv.org/abs/math/0310195 Dimers, Tilings and Trees] | ||
| − | * <br> | + | * [ Conformal invariance of domino tiling]<br> |
** 2000 | ** 2000 | ||
* Kasteleyn, P. W. (1961), "The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice", Physica 27 (12): 1209–1225 | * Kasteleyn, P. W. (1961), "The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice", Physica 27 (12): 1209–1225 | ||
2010년 10월 2일 (토) 04:53 판
introduction
- Gaussian free field [1]http://arxiv.org/abs/math/0312099
- relation to Bethe ansatz http://staff.science.uva.nl/~nienhuis/tiles.pdf
- domino tilings http://www-math.mit.edu/~rstan/transparencies/tilings3.pdf
basic notions
- dimer configurations
- set of dimer configurations
- partition function
- Kasteleyn matrix
physics motivation
Dimer configuration can be considered as the covering of the graph by pairs of fermions connected by an edge
Termperley equivalence
spanning trees on \gamma rooted at x
Dimers on D(\gamma)
Domino tiling and height function
bipartite graph
weight systems
define a weight function on the edges of the graph \gamma
history
encyclopedia
- http://en.wikipedia.org/wiki/Domino_tiling
- http://en.wikipedia.org/wiki/Lozenge
- http://en.wikipedia.org/wiki/Gaussian_free_field
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
expositions
- [2]http://arxiv.org/abs/math/0310326
- 2003
- Lozenge Tiling
- pictures
- http://members.unine.ch/beatrice.detiliere/Cours/Ecole_Doctorale.pdf
articles
- Dimers, Tilings and Trees
- [ Conformal invariance of domino tiling]
- 2000
- Kasteleyn, P. W. (1961), "The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice", Physica 27 (12): 1209–1225
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1214/aop/1019160260
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field